Does Boris-SDC conserve phase space volume?

In this paper we investigate the conservation of phase space volume of the Boris-SDC algorithm. This method provides a generic way to extend the standard, second-order accurate Lorentz force integrator commonly used for charged particles in an electric and magnetic field to a high-order method using spectral deferred corrections. For a single particle in a Penning trap and different frequencies of the electric and magnetic fields, we assess the conservation properties of the method by computing the update matrix of one step of Boris-SDC as well as its determinant. We compare the results to the convergence regions and relate them to energy conservation properties of the method.